Mr Turnbull announced he would resign as the Member for Wentworth in the wake of the Liberal leadership turmoil, forcing a by-election in his safe Liberal seat in Sydney's leafy eastern suburbs.

Shortly after being ousted as Liberal leader, the former prime minister, along with his wife Lucy, jetted off to New York where the pair own an apartment on the upper West Side overlooking Central Park.

Mr Turnbull told an event in Manhattan that he was the first prime minister to have been in favour of same-sex marriage.

"Julia Gillard — whom I admire in many ways — Julia, even though she was living with her boyfriend without the benefit of the closure as it were, for political reasons said 'I believe marriage should be between a man and a woman'.

"And my predecessor and opponent in the Liberal Party, Tony Abbott — who's sort of a right-wing character, to say the least — he had the same view."

"And I was to say they were both wrong, but at least he was sincerely wrong."

Mr Turnbull spruiked what he described as the successful postal plebiscite as a way to navigate the political obstacles in the same-sex marriage debate, and criticised opponents of the process who said it was at risk of having a low participation rate.

"I find it difficult to maintain interest in that political episode because it was so absurd, I can't imagine how boring it will be for everyone here," Mr Turnbull said.

"The bottom line was the remarkable themes, great credit to Australia and Australians, 80 per cent of people voted in a postal ballot that they had no obligations to vote in — they could just as easily throw it into the bin — and about 400,000 or 500,000 young people enrolled to vote.

"And you have people saying 'oh young people don't know what letters are, they won't know how to post them'.

"Lucy and I thought about this, and we said 'they are all young people, they have great eyesight and letter boxes are painted red. They are on street corners'."

Some concerned the Liberals will suffer significant backlash at the Wentworth by-election for ousting a popular local member from the prime ministership.

The former leader's preferred candidate, Dave Sharma, was picked as the Liberal candidate for the poll, to be held on October 20.

Liberal party elders have launched scathing criticisms of Mr Abbott for his role in undermining his successor, and called on him to quit politics.